Quantifying NFT-driven networks in crypto art

The evolution of the art ecosystem is driven by largely invisible networks, defined by undocumented interactions between artists, institutions, collectors and curators. The emergence of cryptoart, and the NFT-based digital marketplace around it, offers unprecedented opportunities to examine the mechanisms that shape the evolution of networks that define artistic practice. Here we mapped the Foundation platform, identifying over 48,000 artworks through the associated NFTs listed by over 15,000 artists, allowing us to characterize the patterns that govern the networks that shape artistic success. We find that NFT adoption by both artists and collectors has undergone major changes, starting with a rapid growth that peaked in March 2021 and the emergence of a new equilibrium in June. Despite significant changes in activity, the average price of the sold art remained largely unchanged, with the price of an artist’s work fluctuating in a range that determines his or her reputation. The artist invitation network offers evidence of rich and poor artist clusters, driven by homophily, indicating that the newly invited artists develop similar engagement and sales patterns as the artist who invited them. We find that successful artists receive disproportional, repeated investment from a small group of collectors, underscoring the importance of artist–collector ties in the digital marketplace. These reproducible patterns allow us to characterize the features, mechanisms, and the networks enabling the success of individual artists, a quantification necessary to better understand the emerging NFT ecosystem.

We find that initial adopters and early majority groups have enjoyed the first movers' advantage in cryptoart.
An examination of the most contested art sold on Foundation (measured by the total number of bids), indicates that most of the bidding took place in the final hour of the bidding timeline (SI Fig 3 A Such patterns of bursty biddings are prevalent across all sold art: the bids come either at the beginning of the auction (a requirement to begin the auction) and at the end of the auction (SI Fig 3 D). As a result, we observe a gradual (and necessary) increase in the auction time for the art that achieves the highest bids Further, new digital art appears to follow an exponential decay in interest from collectors (with decay exponent λ = 0.168). We find that 33.3% of the art receive the first bid within 12 hours of listing and 52.83% receives its first bid within the first two days (Fig 4 A, B). These bidding dynamics also affects the price of the art (Fig 4 C, D). On average, an art that receives a bid within the first two days sells for  $4,276, while an art that receives a bid during the third and fourth day receives $1,628. Taken together, these findings demonstrate the bursty activity of cryptoart, indicating that artworks sold at higher prices (1) feature bidding wars towards the rear end of the auction and (2) the bidding tends to start during the first two days of listing, taking advantage of the novelty of the listed art.

Estimates for scaling coefficient
We estimate the association of followers and their total earning by estimating the scaling coefficient on the log scale regression. First we estimated the overall scaling across all artists and then for each group of artists, finding that the trends hold even when controlled for time of joining, evidence of universality in the scaling features. We present the distributions for each group of artists in SI Fig 5 and the estimates in Table 1. days taken for art to receive its first bid from the time of listing. This appears follows an exponential decay with λ = 0.18 (inset), indicating that novelty of art decays at a fast pace. (B) Time to sell (hours) from the time of listing, finding that majority of the art receives its first bid within the first few hours of listing. (C) Selling price of art based on the number of days it stays on the market before first bid, indicating that NFTs that receive early bids tend to attract high prices. (D) The price differences as a function of time to first bid since listing (hour). These findings highlight that collectors rapidly lose interest in art and an art is more likely to be sold during the first few days of its listing.

Artist Social Network
To list and to sell art on the platform, an artist needs to either (1) be a community upvoted artist (i.e. be popular amongst crypto art enthusiasts) representing 5% of the invites or (2) be invited by an artist or a collector, representing the remaining 95%. While (1) requires prior popularity, (2) is largely driven by offline and online social connections ( Table 2). The number of clusters and the average size of clusters experienced a rapid growth during the early majority and majority period and has remained stable beginning April (SI Fig 6).  Average artist cluster size Figure 6. Growth of the artist network. We find that beginning February 15 up until end of March, the social network had a steep rise in terms of number of artist clusters and the average cluster size but has stabilized beginning June, representing the organic growth of artist clusters.

Local effect of invites
Foundation is an organically growing platform, driven by the ability of the current artists to invite new artists to the platform. The collected data offers an opportunity to ask, how similar are the invited artist to the invitor? We explore this online behavior through multiple facets of artist characteristics: total earning, number of artworks sold, number of Foundation followers, and number of Twitter followers. For each of these node attributes, we conduct random shuffling of values across all nodes and take the average of the 25 generated networks. As an additional randomized version, we also conduct link randomization while preserving the degree of the nodes, thus creating two versions of random reference. We find that artists with higher earning per art tend to invite artists with lower earning per art at a higher rate than expected at random (SI Fig 7 A). In particular, 78.76% of the invited artists had a lower earning per art than the invitor, compared to the randomized expectation of 66.59% of the artists. This translates to an average earning gap of $2,097 per art, while the random experiments estimated an average lower earning of $563.
It is important to highlight that likely the newly invited artists received lower earnings than the artist who invited them due to the temporal nature of invites. That is, the invitor joined the platform prior to the invited artist, allowing the invitor to reap benefit of strong first movers' advantage, as discussed in the manuscript. Furthermore, the difference in earnings between the invited artist and the invitor are small.
These differences are even smaller in the randomized versions ($563), because by randomizing the links we remove the effect of first movers' that allowed some artists to fetch higher prices for their artworks.

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Thus, our finding about the local effect of invites does not contradict the results on homophily in artist invites.
We observe similar features in the number of art sold and Foundation/ Twitter followers, where the invited artist has fewer creations and lower followers respectively than the random realizations ( SI Fig 7   B-D). On average, invited artist tend to sell 2.6 (random: 1.5) fewer art, have 158 (random: 94) fewer Foundation followers, and 3,603 (random: 2,170) fewer Twitter followers. Again, these differences between artists are small and co-exist with our finding that two artists connected by invites are similar in the larger set of parameters defining artistic success. Indeed, the invited artists tend to have similar features to the artist who invited them, indicating that artists tend to invite other artists with a similar perceived earning capacity and reputation. We remove the highest sold artwork in each cluster to evaluate the differences in average earning that is not emphasized due to one time success. The maximum earning per art per artist per cluster is $33,609 (mean: $843) and the randomized versions has a maximum earning of $13899 (mean: $677). Indeed, after removing the highest art sale in each cluster, we find rich clusters that are persistent through multiple high art sales.

Stability in earning
We explore the role of reputation and the sustained ability of high reputation artists to attract high prices.
We provide examples of artists in different groups (SI Fig 9), highlighting that irrespective of the number of artworks sold, artists sell subsequent items in a range derived by the artist reputation.

Artist visibility versus maximum earning
We look at the role of artist reputation on their visibility. We find that artists with high reputation also have high followings, partially explaining their ability to repeatedly attract high prices for artworks (SI Fig 10).

Artist visibility and bidding patterns
We investigate the role of reputation on the attention received on the listed art. We find that high reputation artists not only receive high prices for the works but also attract higher number of bids (SI Fig 11). This effect remains stable throughout their career, highlighting that high reputation artists repeatedly attract higher number of bids for their works. We provide examples comparing the earning capacity for subsequent art sales for artists grouped by different reputation categories. We observe that, while prices changes significantly across subsequent art sales, they fluctuate in a comparable range that determines the artist reputation. That is high reputation artists repeatedly receive high prices for their works, while low reputation artists struggle to attract high prices.

Peak art success
The timing of highest sale (t * , peak art price) is found to occur a random point in the career of an artist and is similar to the random career permutations ( SI Fig 12 A), a pattern similar to the ones seen in scientific careers. Yet, high impact artists find their success earlier in their career compared to the medium and low impact artists (SI Fig 12 B). The average sale price of the highest sold art is significantly higher compared to the previous and subsequent art sale price ( SI Fig 12 C). This indicates that there are no recognizable changes in the price leading up to and following the peak artist success.

Collector growth
The collector growth can be characterized by measuring the number of new collectors (N collector ) that invest an artist's work. In other words, it allows us to measure the effect of repeat collectors for an artist. . Artist follower counts its impact on max art sale. We find that number of Foundation followers scales linearly with the maximum selling price of art (β = 0.935), indicating that highly popular artists also attract high prices. Further, we observe a separation based on the categorized reputation level (low max earning, medium max earning, high max earning), indicating that artist reputation is correlated with artist visibility.
We find that all artists, irrespective of their reputation, acquire new buyers at a slow rate (SI Fig 13), highlighting the importance of returning collectors in artist career. Average number of bids Figure 11. Artist visibility and its impact on bidding. We find that the high reputation artists continue to receive higher number of bids for their work. The shaded region represents the randomized careers (95% confidence interval) while the symbols indicate actual values. The timing of highest art sale price (t * ) for artists (star) and the random realizations (circle). We find no significant difference the timing of highest sale (Mann Whitney U Test; p val = 0.33), supporting the claim that artists may find their highest sale at any art sale. The drop off at the 6th art sale is due to the filtering of artists with atleast 6 sales. (B) Average selling price of art prior to and following the highest art sale (N * ). There exists no discernible differences in the artist success leading up to and after the highest art sale. (C) The location of the highest art sale in the artist career (N * /N). The high impact artists appear to find their peak success early in their career compared to the medium and high impact groups.  Figure 13. Artist collector growth. We find that all artists attract repeated collectors indicating a slow growth rate in the collector base. The symbols indicate the empirical average of collector growth while the shaded region show the randomized career permutations (85% confidence interval), and lines indicates the growth rate where each art is bought by a new collector.